V'(t) = -250(1-(1/40)t)
If we know the time, we can plug in the value for "t" in the above derivative and find how much water drained for the given point of t.
Given:
V =2000( 1- (1/40)t)^2 , where 0≤t≤40.
Here we have to find the derivative with respect to "t"
We have to use the chain rule to find the derivative.
V'(t) = 2 (2000)(1- (1/40)t)d/dt(1- (1/40)t)
V'(t) = 2(2000)(1-(1/40)t(-1/40)
When we simplify the above, we get
V'(t) = -250(1-(1/40)t)
If we know the time, we can plug in the value for "t" and find how much water drained for the given point of t.
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Write an expression for the volume of a cube with a side of length 3z^5 Simplify your expression
The volume of the cube is 27[tex]z^{15}[/tex]
A cube is a three dimensional shape having 6 square faces , all the faces are of equal length , breadth and height.
Here we have to find the volume of a cube
The length of the side is 3[tex]z^{5}[/tex].
The formula for the volume of the cube = a³
where a is the length of the side.
Substituting the value of a we get,
The volume of the cube = (3[tex]z^{5}[/tex])³
= 27[tex]z^{15}[/tex]
Therefore the volume of a cube is 27[tex]z^{15}[/tex].
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What polynomial identity should be used to prove that 61 = 125 − 64?
a
Difference of Cubes
b
Difference of Squares
c
Square of a Binomial
d
Sum of Cubes
The polynomial identity can be used to prove that 61 = 125 − 64 is the difference between cubes therefore, option (a) is correct.
What is a number system?The number system is a way to represent or express numbers.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
As per the given polynomial,
61 = 125 - 64
It is known that a³ = a × a × a
Therefore, 5³ = 5 × 5 × 5 = 125
And, 4³ = 4 × 4 × 4 = 64
Therefore, 61 = 5³ - 4³
Hence "The polynomial identity can be used to prove that 61 = 125 − 64 is the difference between cubes".
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1) Calculate the perimeter of
this triangle
7cm
4cm
10cm
6cm
Answer:
23cm
Step-by-step explanation:
in this problem the 4cm actually doesnt matter. so what you can dois 7cm+6cm+10cm=answer
7cm+6cm+10cm=23cm
Write 72.4% as a decimal
Answer:
0.724
Step-by-step explanation:
percent means ' out of 100 ' , then
72.4% = [tex]\frac{72.4}{100}[/tex] = 0.724
Triangle rst is rotated 180° about the origin, and then translated up 3 units. Which congruency statement describes the figures? δrst ≅ δacb δrst ≅ δabc δrst ≅ δbca δrst ≅ δbac.
Triangle RST is rotated 180° about the origin, and then translated up 3 units. Then , ΔRST ≅ ΔBAC
We know that To rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y).
Thus, The coordinates of triangle RST becomes
R (1,1) → R'(-1,-1)
S (3,4) → S'(-3,-4)
T(-5,0) → T'(5,0)
Also ΔRST after rotation is translated up 3 units. , so we apply the rule (x,y)→(x,y+3)
R'(-1,-1)→R"(-1,-1+3)=R"(-1,2)→ B
S'(-3,-4) → S"(-3,-4+3) = R"(-3,-1) → A
C'(-5,0) → C"(-5,0+3) → C"(-5,3) → C
As rotation and translation both are rigid transformation that maps only congruent figures.
Therefore, ΔRST ≅ Δ BAC
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pls help its urgent!!
Suppose that R and S are points on the number line If RS= 10 and R lies at 13 where could S be located
Considering that R and S are points on the number line If RS= 10 and R lies at 13 then s will lie at
323'What is a number line?A number line is a sequence of numbers arranged at a particular pattern in a straight line
How to find the point of S if R lies at point 13Information gotten form the question have it that"
RS= 10
R lies at 13
In a number line if R lies in point 13 and RS = 10 then we solve as follows
R + | 10 |
13 + 10 = 23
13 - 10 = 3
Hence R lies at point 3 or 13
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The cost of renting a canoe to use on River Y costs $.40 The cost of renting a canoe to use on River Z costs $5 per hour plus a $15 deposit. The total cost, c, of renting a canoe on either river for n hours can be represented by an equation. Write and graph a system to find how many hours you have to rent a canoe for the cost to be the same on both rivers.
Answer:
y=40 z= 5h+15
5 hours to make the same amount of money
Step-by-step explanation:
40-15=25
25/5=5
hope this helped
ASAP!!!
2 1/4x + 1/2x = 44
Solove for X and include all steps to get branliest.
Answer:
16
Step-by-step explanation:
→ Add the fractions
[tex]2\frac{1}{4} +\frac{1}{2} =\frac{9}{4} +\frac{1}{2} =\frac{9}{4} +\frac{2}{4} =\frac{11}{4}[/tex]
→ Equate to 44
[tex]\frac{11}{4} x=44\\[/tex]
→ Multiply both sides by 4
11x = 176
→ Divide both sides by 11
x = 16
Find the sum of 8x^{2}-x+98x
2
−x+9 and 8x^{2}-5x+58x
2
−5x+5.
Answer: 16x^2+144x+18
Step-by-step explanation:
The sum of two given expressions is 16x²-6x+14.
What is addition of algebraic expression?Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems.
The given expressions are 8x²-x+9 and 8x²-5x+5.
Now, sum =8x²-x+9+8x²-5x+5
Group like terms and simplify, we get
(8x²+8x²)+(-x-5x)+(9+5)
= 16x²+(-6x)+14
= 16x²-6x+14
Therefore, the sum of two given expressions is 16x²-6x+14.
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Main has $36 to spend on movie tickets. Each movie ticket costs $4.50. How many tickets can she buy? Write a multiplication equation and division equation to represent this situation.
Answer:
Main can buy 8 tickets.
Step-by-step explanation:
Use the equation total amount ÷ cost of each ticket
Input your information: $36 ÷ $4.50
The equation adds up to 8.
So therefore, Main can buy 8 tickets.
How to find the square root of [tex]\sqrt{28[/tex]
The value of square root of √28 will be;
⇒ 4√7 = 5.28
What is square root of a number?
A square root of a number is a value that multiplied by itself gives the same number.
Given that;
The number is,
⇒ √28
Now,
Let the value of square root of √28 is find as;
Since,
28 = 2 x 2 x 7
Hence,
⇒ √28 = √2 x 2 x 7
⇒ √28 = 2√7
⇒ √28 = 2 x 2.64
⇒ √28 = 5.28
Therefore,
The value of square root of √28 will be;
⇒ 4√7 = 5.28
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Jeffrey rolled a 12-sided dice 15 times. It landed on a number greater than 10 three times. How
does the experimental probability of Jeffrey's rolls compare to the theoretical probability of
rolling a number greater than 10?
The experimental probability of the roll is greater than the theoretical probability
How to compare the experimental probability and theoretical probability?
Probability is the likelihood of a desired event happening.
Experimental probability is a probability that relies mainly on a series of experiments.
Theoretical probability is the theory behind probability. To find the probability of an event, an experiment is not required. Instead, we should know about the situation to find the probability of an event occurring.
Given that:
Jeffrey rolled a 12-sided dice 15 times and it landed on a number greater than 10 three times
Experimental probability = 3/15 = 1/5
But theoretically, a number greater than 10 in 12-sided dice have the probability of 2 out of 12 as illustrated with the numbers below:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Theoretical probability = 2/12 =1/6
Therefore, the experimental probability (1/5) of rolling a number greater than 10 is greater than the theoretical probability (1/6)
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if the measure of angle ADC is 59 , what is the measure of angle BDC
The angle of BDC is 60 degrees.
The Angle Sum Property: What Is It?The angle sum property of a triangle states that the sum of a triangle's three internal angles is 180 degrees. A triangle is a closed figure made up of three line segments that have both internal and external angles. When the values of the other two angles are known, the measure of an unknown interior angle can be determined using the angle sum property.
The data listed above can be inserted into our diagram. ADB and BDC complement one another, therefore their combined degree measurement is 180. Thus, m∠ADB is equal to 180 – 60, or 120 degrees.
Given,
∠ADC = 59
∠BDC = ?
∠ADB = ∠BCD
∠BCD = 90
∠ADB = 90
∠ADC = 59
∠ADB + ∠BDC = 59
90 + ∠BDC = 59
∠BDC = -31
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How to turn “the number with the units digit equal to x and the tens digit three more than the ones digit” into a algebraic problem
The number with the unit digit equal to x and the tens digit three more than the one's digit is; 30 + 11 X
How to identify the place value of a digit in a number?The place values on the left of the decimal point start as ones, tens, hundreds, and so on. The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths so on...
Given the statement as“the number with the units digit equal to x and the tens digit three more than the ones digit”
We need to convert the statement into the algebraic expression.
We know that unit digit number = X × 1
Then Tens digit number = (3 + X ) 10
Thus, the number = 30 + 10X + X
Hence, the Number = 30 + 11 X
The number with the unit digit equal to x and the tens digit three more than the one's digit is; 30 + 11 X
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Consider the points on a line segment in the coordinate plane A(-2, -4) and B(0, 8). What is the
distance from the midpoint to the origin?
A √8
B √5
C √10
D √2
The distance from the midpoint to the origin is [tex]\sqrt{5}[/tex].
What is midpoint?
Midpoint is the point that is in the middle pf the line, and to calculate midpoint the formula is
[(x)1 + (x)2]/2, [(y)1 + (y)2]/2
given coodinates are (-2, -4) and (0, 8)
midpoint = (-2+0/2, 8-4/2)
=(-1, 2)
to find the distance from the midpoint to origin.
d= [tex]\sqrt{(x_{2}-x_{1} )^2+(y_{2} -y_{2} )^2} }[/tex]
the points are (-1,2) and (0,0)
d = [tex]\sqrt{(-1)^2+(2)^2}[/tex]
d = [tex]\sqrt{5}[/tex]
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Write the inequality for the statement: the difference between a number and seven eighths exceeds negative two thirds f plus 7 over 8 is greater than 2 over 3 f minus 7 over 8 is less than or equal to negative 2 over 3 f minus 7 over 8 is greater than negative 2 over 3 f minus 7 over 8 is less than negative 2 over 3
The inequality for the statement: the difference between a number and seven eighths exceeds negative two thirds is g - 7/8 > -2/3.
The correct answer option is option c
How to write inequality equation?Let
The unknown number = gdifference between a number and seven eighths
g - 7/8
difference between a number and seven eighths exceeds negative two thirds
g - 7/8 > -2/3
The options;
A. g plus 7 over 8 is greater than 2 over 3
g + 7/8 > 2/3
B. g minus 7 over 8 is less than or equal to negative 2 over 3
g - 7/8 ≤ -2/3
C. g minus 7 over 8 is greater than negative 2 over 3
g - 7/8 > -2/3
D. g minus 7 over 8 is less than negative 2 over 3
g - 7/8 < -2/3
So therefore, the inequality statement can be written as g - 7/8 > -2/3.
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Which represents the inverse of the function f(x)
4x?
O h(x) = x + 4
O h(x) = x -4
O h(x) = ›
h(x) = #x
Answer: Summary: The equation which represents the inverse of the function f(x) = 4x is h(x) = 1/4 x.
Step-by-step explanation: THERE IS NO EXPLANATION
(hope this helps) :)
What is 1 as a power of 10
Answer:
Step-by-step explanation:
1 to the 10th power is 1.
Convert the following repeating decimal to a fraction in simplest form .38
The answer is : 7/18
Step by step:
(0.38 x 10) - 0.3/9
3.5 = 35
---- ----
9 90
= 7/18
DOI HAVE TO DISTRIBUTE?
2+5(x+3)-3(x-4)=x+2(2x+4)
Answer:
Yes, you have to distribute.
Step-by-step explanation:
2+5(x+3)-3(x-4)=x+2(2x+4)
2+5x+15-3x+12=2(2x+4)
Add the Numbers
2+5x-3x=2(2x+4)
Combine Like Terms, Then you can rearrange the terms for simplification. You should end up with an exation looking like this:
2x+29=5x+8
Subtract 29 from both sides. Simplify, then subtract 5x from both sides.
2x-5x=5x-21-5x
Simplify, then Divide both sides by the same factor. Simplify once more then you should have
x=7
Hope this helps ;)
3 c = (2b²)
What is this
Step-by-step explanation:
I hope this helps you with your answer
Lena is building a fence. She will need to dig up holes to help support the posts that hold up the fence. The holes need to have a depth of 3 1/3 feet below the ground. Each post is 10 feet long. What is the height of the part of the post that is above the ground? PLEASE HELP 100 points
The height of the part of the post that is above the ground is 10 - 3(1/3)
= 6(2/3) feet.
What is a height?Height is degree of vertical distance, both vertical extent (how "tall" some thing or a person is) or vertical position (how "high" a factor is). For example, "The peak of that constructing is 50 m" or "The peak of an aircraft in-flight is ready 10,000 m". For example, "Christopher Columbus is five foot 2 inches in vertical peak."When the time period is used to explain vertical position (of, e.g., an aircraft) from sea level, peak is greater frequently referred to as altitude.Furthermore, if the factor is connected to the Earth (e.g., a mountain peak), then altitude (peak above sea level) is referred to as elevation.In a two-dimensional Cartesian space, peak is measured alongside the vertical axis (y) among a particular factor and every other that doesn't have the identical y-value. If each factors occur to have the identical y-value, then their relative peak is zero. In the case of 3-D space, peak is measured alongside the vertical z axis, describing a distance from (or "above") the x-y plane.To learn more about height from the given link:
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If line q bisects KM at point V, KV = 2.5z,
and VM = 5z - 10, find KM. No
The value of KM is 20
What is segment bisector ?A line, ray, line segment, or point that cuts a line segment at its center and divides it into two equal portions is known as a segment bisector. A segment is a section of a line with definite ends, which is also how the word segment is sometimes used. Any object or line is divided into two equal halves when it is bisected. Consequently, when two line segments cut or bisect each other at a location that divides the lines into equal halves, this is known as a segment bisector.
Given that : The line q bisects KM at point V, KV = 2.5z and VM = 5z - 10
the line q bisects KM at point V so KV = VM
KV = 2.5z
VM = 5z - 10
2.5z= 5z - 10
10 = 2.5z
4 = z
Now put the value of 4 in KV and VM
KV = 2.5(4)
VM = 5(4) - 10
KV + 10
VM = 10
KM = KV + VM
KM = 10 + 10
= 20
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A woman has a total of $8,000 to invest. She invests part of the money in an account that pays 11 % per year
and the rest in an account that pays 12% per year. If the interest earned in the first year is $920, how much did
she invest in each account?
Answer:
Step-by-step explanation:
art I 5.00% per annum ------------- Amount invested =x
Part II 9.00% per annum ------------ Amount invested = y
8000
Interest----- 520.00
Part I 5.00% per annum ---x
Part II 9.00% per annum ---y
Total investment
x + 1 y= 8000 -------------1
Interest on both investments
5.00% x + 9.00% y= 520
Multiply by 100
5 x + 9 y= 52000.00 --------2
Multiply (1) by -5
we get
-5 x -5 y= -40000.00
Add this to (2)
0 x 4 y= 12000
divide by 4
y = 3000
Part I 5.00% $ 5000
Part II 9.00% $ 3000
CHECK
5000 --------- 5.00% ------- 250.00
3000 ------------- 9.00% ------- 270.00
Total -------------------- 520.00
The function H(X) equals 0.6X plus 3.8 models the height in inches of a stack of X cups. What key features is at H(0)?
The key feature of the function H(X) = 0.6X + 38 at H(0) is 3.8
Function:
A function is defined as the an expression, rule, or law that defines a relationship between one independent variable and another dependent variable.
Given,
Here we have the function H(X) = 0.6X + 3.8 models the height in inches of a stack of X cups.
And we need to find the key features is at H(0).
To find the key feature at H(0), then we have to simple apply the value of X as 0,
Like the following, we have to replace the X value in the function with 0, then we get the expression like the following,
=> H(0) = 0.6(0) + 3.8
=> H(0) = 0 + 3.8
H(0) = 3.8
Therefore, the key feature at H(0) is 3.8.
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a politician who is running for the office of governor of a state with 4 million registered voters commissions a survey. in the survey, 54% of the 5,000 registered voters interviewed say they plan to vote for her. the population of interest is the:
a. 4 million registered voters in the state where the 5,000 registered voters is drawn from the pool of registered voters.
Options: a. 4 million registered voters in the state
b. 5,000 registered voters interviewed
c. 54 %, voters interviewed who plan to vote for him
d. 46 %, voters interviewed who plan not to vote for him
The population of interest is the group from which a sample set is collected. Here, the 5,000 registered voters is drawn from the pool of registered voters. The people surveyed are representative of the total number of voters. The population of interest here is the 4 million registered voters.
For example, if a survey is carried out to figure out the age that kids start walking, the population of interest is kids in general and not just the children who are surveyed.
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Graph the polygon with the given vertices and its image after a reflection in the line y=-x . A(0, -3), B(2, 2), C(5,\0)
The reflection of a coordinate about the y = x will interchange the coordinate thus the reflection of points A(0, -3), B(2, 2), C(5,0) will be A'(-3,0)B'(2,2)C',(0,5).
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
Reflection is a mirror image of a graph about any axis.
It is known that,
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
Therefore,
A(0, -3) → A'(-3,0)
B(2, 2) → B'(2,2)
C(5,0) →C'(0,5)
Hence "The reflection of a coordinate about the y = x will interchange the coordinate thus the reflection of points A(0, -3), B(2, 2), C(5,0) will be A'(-3,0)B'(2,2)C',(0,5)".
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1 7
_ + _
6 10
Ayuda por favor
Answer: no entiendo la estructura de la operacion
Step-by-step explanation:
name the sampling method used in this data collection. a polling company wanted to study about hr personnel in tech companies. the pollster selects five tech companies and interviews all hr personnel in each of the 5 companies.
Cluster Sample is the sampling method used in this type of data collection.
Cluster sampling is a sampling technique used in statistics that divides the total population under consideration into externally homogeneous but internally heterogeneous groupings known as clusters. Each cluster essentially serves as a miniature representation of the overall population.
Using simple random sampling, some clusters are picked after the clusters have been identified, while the remaining clusters are left out of the study. A researcher must determine the right sampling strategy for each cluster after identifying the clusters.
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